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Scaling and criticality in a stochastic multi-agent model of a financial market

Nature volume 397, pages 498–500 (1999)Cite this article

Abstract

Financial prices have been found to exhibit some universal characteristics1,2,3,4,5,6 that resemble the scaling laws characterizing physical systems in which large numbers of units interact. This raises the question of whether scaling in finance emerges in a similar way — from the interactions of a large ensemble of market participants. However, such an explanation is in contradiction to the prevalent ‘efficient market hypothesis’7 in economics, which assumes that the movements of financial prices are an immediate and unbiased reflection of incoming news about future earning prospects. Within this hypothesis, scaling in price changes would simply reflect similar scaling in the ‘input’ signals that influence them. Here we describe a multi-agent model of financial markets which supports the idea that scaling arises from mutual interactions of participants. Although the ‘news arrival process’ in our model lacks both power-law scaling and any temporal dependence in volatility, we find that it generates such behaviour as a result of interactions between agents.

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Figure 1: Typical ‘snapshot’ from a longer simulation run.
Figure 2: Log-log plot of the complement of the cumulative distribution of returns (ret.) at different levels of time aggregation: ret.(τ) = ln(pτ) − ln(pt−τ).
Figure 3: Estimation of self-similarity parameter H.

References

  1. Mandelbrot, B. The variation of certain speculative prices. J. Bus. 35, 394–419 (1963).

    Article  Google Scholar 

  2. Fama, E. Mandelbrot and the stable Paretian hypothesis. J. Bus. 35, 420–429 (1963).

    Article  Google Scholar 

  3. Mantegna, R. N. & Stanley, E. Scaling behaviour in the dynamics of an economic index. Nature 376, 46–49 (1995).

    Article  ADS  CAS  Google Scholar 

  4. Ghashgaie, S., Breymann, W., Peinke, J., Talkner, P. & Dodge, Y. Turbulent cascades in foreign exchange markets. Nature 381, 767–770 (1996).

    Article  ADS  Google Scholar 

  5. Galluccio, S., Caldarelli, G., Marsili, M. & Zhang, Y. -C. Scaling in currency exchange. Physica A 245, 423–436 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  6. Liu, Y., Cizeau, P., Meyer, M., Peng, C. -K. & Stanley, H. E. Correlations in economic time series. Physica A 245, 437–440 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  7. Fama, E. Efficient capital markets: a review of theory and empirical work. J. Fin. 25, 383–417 (1970).

    Article  Google Scholar 

  8. Shleifer, A. & Summers, L. H. The noise trader approach to finance. J. Econ. Perspect. 4, 19–33 (1990).

    Article  Google Scholar 

  9. Palmer, R. G., Arthur, W. B., Holland, J. H., LeBaron, B. & Tayler, P. Artificial economic life: a simple model for a stockmarket. Physica D 75, 264–274 (1994).

    Article  ADS  Google Scholar 

  10. Levy, M., Levy, H. & Solomon, S. Microscopic simulation of the stock market: the effect of microscopic diversity. J. Phys. I (France) 5, 1087–1107 (1995).

    Article  Google Scholar 

  11. Bak, P., Paczuski, M. & Shubik, M. Price variations in a stock market with many agents. Physica A 246, 430–453 (1997).

    Article  ADS  Google Scholar 

  12. Caldarelli, G., Marsili, M. & Zhang, Y. -C. Aprototype model of stock exchange. Europhys. Lett. 40, 479–484 (1997).

    Article  ADS  CAS  Google Scholar 

  13. Brock, W. & LeBaron, B. Adynamical structural model for stock return volatility and trading volume. Rev. Econ. Stat. 78, 94–110 (1996).

    Article  Google Scholar 

  14. Brock, W. & Hommes, C. Rational routes to randomness. Econometrica 65, 1059–1095 (1997).

    Article  MathSciNet  Google Scholar 

  15. Lux, T. Time variation of second moments from a noise trader/infection model. J. Econ. Dyn. Control 22, 1–38 (1997).

    Article  MathSciNet  Google Scholar 

  16. Lux, T. The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions. J. Econ. Behav. Organizat. 33, 143–165 (1998).

    Article  Google Scholar 

  17. Guillaume, D. M.et al. From the bird's eye to the microscope: a survey of new stylized facts of the intra-daily foreign exchange markets. Fin. Stoch. 1, 95–129 (1997).

    Article  Google Scholar 

  18. Gopikrishnan, P., Meyer, M., Amaral, L. A. N. & Stanley, H. E. Inverse cubic law for the distribution of stock price variations. Eur. Phys. J. B 3, 139–140 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Peng, C. -K.et al. Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689 (1994).

    Article  ADS  CAS  Google Scholar 

  20. Lux, T. Long-term stochastic dependence in financial prices: evidence from the German stock market. Appl. Econ. Lett. 3, 701–706 (1996).

    Article  Google Scholar 

  21. Platt, N., Spiegel, E. A. & Tresser, C. On-off intermittency: a mechanism for bursting. Phys. Rev. Lett. 70, 279–282 (1993).

    Article  ADS  CAS  Google Scholar 

  22. Haegy, J. F., Platt, N. & Hammel, S. M. Characterization of on-off intermittency. Phys. Rev. E 49, 1140–1150 (1994).

    Article  ADS  Google Scholar 

  23. Youssefmir, M. & Huberman, B. Clustered volatility in multiagent dynamics. J. Econ. Behav. Organizat. 32, 101–118 (1997).

    Article  Google Scholar 

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Acknowledgements

Financial support by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn is acknowledged.

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Authors and Affiliations

  1. Department of Economics, University of Bonn, Adenauerallee 24‐42, 53113, Bonn, Germany

    Thomas Lux

  2. Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d'Armi, 09123, Cagliari, Italy

    Michele Marchesi

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  1. Thomas Lux
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  2. Michele Marchesi
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Correspondence to Thomas Lux.

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Lux, T., Marchesi, M. Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397, 498–500 (1999). https://doi.org/10.1038/17290

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